There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM spac...There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.展开更多
Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Bana...Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.展开更多
In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） ...In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras.展开更多
Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defin...Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.展开更多
文摘There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.
文摘Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.
基金supported by Korea Science & Engineering Foundation (Grant No. F01-2006-000-10111-0)
文摘In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras.
文摘Based on the isomorphism between the space of star-shaped sets and the space of continuous positively homogeneous real-valued functions, the star-shaped differential of a directionally differentiable function is defined. Formulas for star-shaped differential of a pointwise maximum and a pointwise minimum of a finite number of directionally differentiable functions, and a composite of two directionaUy differentiable functions are derived. Furthermore, the mean-value theorem for a directionaUy differentiable function is demonstrated.
